High-Flying Cliff Divers: Calculating Time and Distance

How much time does it take the cliff divers to reach the water?

The cliff divers are jumping off a cliff that is 53.0 m high and travel 17 m horizontally while diving. How long does it take for them to reach the water?

Answer:

It takes the cliff divers 2.17 seconds to reach the water.

The cliff divers jumped off from a cliff that is 53.0 m high and travel 17 m horizontally. The question asks how much time it takes for the cliff divers to reach the water.

To answer the question, we can use the kinematic equation that involves displacement, initial velocity, final velocity, acceleration, and time. In this problem, we know the initial velocity is zero since the cliff divers started from rest and the acceleration due to gravity is -9.8 m/s² since the divers are falling towards the earth.

Let's solve for the final velocity: vf^2 = vi^2 + 2ad

Where: vf = final velocity vi = initial velocity a = acceleration d = displacement

vf^2 = (0 m/s)^2 + 2(-9.8 m/s^2)(53.0 m) vf^2 = -1039.4 m^2/s^2 vf = -32.2 m/s

Since the acceleration is negative, this means that the velocity is decreasing. Now we can use another kinematic equation that involves displacement, initial velocity, final velocity, and time. Let's solve for time: t = (d - vi * t) / v

final velocity is negative because it is going downwards, so we need to use its magnitude, which is 32.2 m/s t = 70 m / 32.2 m/s t = 2.17 s

Therefore, it takes the cliff divers 2.17 seconds to reach the water.